English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Based on the technique of integration within an ordered product (IWOP) ofoperators we introduce the Fresnel operator for converting Caldirola-KanaiHamiltonian into time-independent harmonic oscillator Hamiltonian. The Fresneloperator with the parameters A,B,C,D corresponds to classical optical Fresneltransformation, these parameters are the solution to a set of partialdifferential equations set up in the above mentioned converting process. Inthis way the exact wavefunction solution of the Schr\"odinger equation governedby the Caldirola-Kanai Hamiltonian is obtained, which represents a squeezednumber state. The corresponding Wigner function is derived by virtue of theWeyl ordered form of the Wigner operator and the order-invariance of Weylordered operators under similar transformations. The method used here can besuitable for solving Schr\"odinger equation of other time-dependentoscillators.

Fresnel operator, squeezed state and Wigner function for Caldirola-Kanai Hamiltonian